Lakshmibai-Seshadri Paths and Non-Symmetric Cauchy Identity

Abstract

We give a simple crystal theoretic interpretation of the Lascoux’s expansion of a non-symmetric Cauchy kernel \({\prod }_{i+ j \leq n + 1}(1-x_{i}y_{j})^{-1}\), which is given in terms of Demazure characters and atoms. We give a bijective proof of the non-symmetric Cauchy identity using the crystal of Lakshmibai-Seshadri paths, and extend it to the case of continuous crystals.

Keywords

Quantum groups Crystals Demazure modules

Presented by Anne Schilling.

This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1501-01.